The Magic of Universal Quantum Computing with Permutations

The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject). A first classification of a few types of resulting magic states in low dimensions d≤9 is performed.

DISCRETE COHERENT STATES FOR n QUBITS

Discrete coherent states for a system of n qubits are introduced in terms of eigenstates of the finite Fourier transform. The properties of these states are pictured in phase space by resorting to the discrete Wigner function.